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Phy 121
Your 'cq_1_26.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A simple pendulum has length 2 meters. It is pulled back 10 cm from its equilibrium position and released. The tension in the string is 5 Newtons.
•Sketch the system with the pendulum mass at the origin and the x axis horizontal.
answer/question/discussion: ->->->->->->->->->->->-> :
If it is pulled back 10 cm, then it has a x component of -10 cm. The y component is 2 m, which is 200 cm.
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•Sketch a vector representing the direction of the pendulum string at this instant. As measured from a horizontal x axis, what is the direction of this vector? (Hint: The y component of this vector is practically the same as the length; you are given distance of the pullback in the x direction. So you know the x and y components of the vector.)
answer/question/discussion: ->->->->->->->->->->->-> :
It has x component = -10 cm and y component = 200 cm, therefore the direction and degree value = arctan(200 cm / -10 cm) = 96.86 degrees in the counterclockwise direction from the positive x axis.
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•What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
Wouldn't this also be the same as the pendulum string vector? That would be 92.86 degrees in the counterclockwise direction from the positive x axis.
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•What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
I want to say that the -10 cm and 200 cm are the x and y components of the vector, but it just hit me that for each unit of measure (like force, changte in distance, or velocity) have their own x and y components.
With this now clicked in my brain I will say that the x component = L * cos(92.86 degrees) = -0.25 Newtons and the y component = L * sin(92.86 degrees) = 4.99 Newtons
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•What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> :
Well if the force = 5 Newtons and the acceleration is 9.8 m/s^2 from the gravitational force, then the mass is 5 Newtons / 9.8 m/s^2 = 0.5 kg
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•What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
Well the Fnet = 5 N and the mass = 0.5 kg, therefore the a = Fnet / m = 5 Newtons / 0.5 kg = 10 m/s^2
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It's only the x component of the tension that accelerates the pendulum. The y component of the tension is, except for a negligible amount, equal to the weight of the pendulum.
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See my note immediately above, then check out the discussion at the link below. No need to resubmit:
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
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